tailieunhanh - Báo cáo hóa học: " Research Article Well-Posedness and Fractals via Fixed Point Theory"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Well-Posedness and Fractals via Fixed Point Theory | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 645419 9 pages doi 2008 645419 Research Article Well-Posedness and Fractals via Fixed Point Theory Cristian Chifu and Gabriela Petrusel Department of Business Faculty of Business Babeậ-Bolyai University Cluj-Napoca Horea 7 400174 Cluj-Napoca Romania Correspondence should be addressed to Gabriela Petrusel gabip@ Received 25 August 2008 Accepted 6 October 2008 Recommended by Andrzej Szulkin The purpose of this paper is to present existence uniqueness and data dependence results for the strict fixed points of a multivalued operator of Reich type as well as some sufficient conditions for the well-posedness of a fixed point problem for the multivalued operator. Copyright 2008 C. Chifu and G. Petrusel. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Let X d be a metric space. We will use the following symbols see also 1 P X Y c X Y 0 Pb X Y e P X Y is bounded Pcl X Y e P X Y is closed Pcp X Y e P X Y is compact . If T X P X is a multivalued operator then for Y e P X T Y UxeYT x we will denote the image of the set Y through T. Throughout the paper FT x e X x e T x resp. SF T x e X x T x denotes the fixed point set resp. the strict fixed point set of the multivalued operator T. We introduce the following generalized functionals. The Ô generalized functional ỗd P X X P X - R u ôd A B sup d a b a e A b e B . 2 Fixed Point Theory and Applications The gap functional Dd P X X P X - R u to 2 . . _ Dd A B inf d a b a e A b e B . The excess generalized functional Pd P X X P X - R u to _ n Pd A B sup Dd a B a e A . The Pompeiu-Hausdorff generalized functional Hd P X X P X - R u to Hd A B max pd A B pd B A . The first purpose of this paper is to present existence uniqueness and .

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